The "political spectrum" is often expanded from a one dimensional scale from left to right to a two dimensional system on axes such as social policy or fiscal policy. Whatever the axes it is a useful metaphore.

Below are simulations of elections based on putting voters and candidates in a two dimensional space of political thinking. Candidates take various positions (indicated by diamonds) and voters tend to vote for the closest candidates. The graphs are made by simulating a voting populace centered at each point in the image. Diversity in the voters is over a gaussian distribution around that center. This randomness causes some fuzz in the graphs in regions where an election method is sensitive enough to that noise to occasionaly flip the result.

Results here, or the same configurations zoomed out a factor of ten. Also, a run with linear preference falloff, 1-r instead of 1/r. A couple runs with ten choices splitting and fracturing the voting populace in some complex ways.

I did a couple series of small multiples: three choices, two held stationary, one moving; four choices, varying population distribution grouping tightness.

multi-winner elections show that Single Transferrable Vote has some oddities just like IRV.There is a public read-only subversion repository, check it out with:

svn co http://voteutil.googlecode.com/svn/sim_one_seat

Some notes on the source code. An example election method implementation.